Quartz crystal microbalances (QCM) have been extensively used in sensing the mass loading with extremely high sensitivity (<10 ng/cm2). A QCM device typically consists of a thin disk of AT-cut quartz crystal with circular electrodes patterned on both sides. Due to the piezoelectric properties and crystalline orientation of the quartz, the alternating voltage between the electrodes results in a shear waves within the crystal. For this reason, QCM is sometimes referred to as a thickness shear mode resonator (TSM)) in the literature. With a film with certain mass attached on one side of the electrode, the resonant properties such as resonant frequency and bandwidth of the QCM will be changed accordingly.
The relationship between the resonant frequency shift, Δf, and surface mass density, Δm/A of a thin and rigid film on QCM, can be expressed as Sauerbrey theory
                              Δ          ⁢                                          ⁢          f                =                              1            C                    ⁢                                    Δ              ⁢                                                          ⁢              m                        A                                              (        1        )            where C is the mass sensitivity coefficient which is given by
                    C        =                                                            μ                q                            ⁢                              ρ                q                                                          2            ⁢                          f              2                                                          (        2        )            where ρq is the density of quartz crystal, μq is the shear modulus of quartz crystal, and f0 is resonant frequency of the QCM without mass loading.
Substituting Eqn. (2) into Eqn. (1), one obtains Eqn. 3):
                              Δ          ⁢                                          ⁢          f                =                              -                                          2                ⁢                                  f                  0                  2                                                                                                  μ                    q                                    ⁢                                      ρ                    q                                                                                ⁢                                    Δ              ⁢                                                          ⁢              m                        A                                              (        3        )            
The mass loading on the QCM normally results in a negative resonant frequency shift, as illustrated by the negative sign.
For a typical 10 MHz QCM, the value of C is 4.42 ng/cm2/Hz. As indicated by Eqn. (2), a higher resonant frequency is needed to achieve better sensitivity of QCM. Unfortunately, a higher resonant frequency requires a thinner quartz crystal, which makes the crystal become extremely fragile and the high resonant frequency also leads to higher energy dissipation when the QCM operate in a liquid environment.
In applications such as QCM based biosensors, one side electrode is usually functionalized by coating a thin film of polymer to attach biomolecules. However, the sensitivity of the QCM is compromised since the signal of the QCM could be significantly damped down due to the viscoelastic response of the polymer to the acoustic wave transmission. The situation may get much worse with the increasing of the film thickness. Intensive research effort has been concentrated on utilizing micro- and nano-scale structures to increase the sensing area of QCM in order to improve the response of QCM. Special fabrication techniques are required for these micro/nanostructures, which furthermore result in sophisticate structure-acoustic wave interactions. This makes the signal analysis very challenging.
Sauerbrey theory (as expressed by Eqn. (1)), indicates negative resonant frequency shift resulted from the mass loading on QCM. However, Dybward first reported an increased resonant frequency with gold spheres (10-50 μm in diameter) placed on the surface of a QCM device, and the increase of resonant frequency was dependent of the bonding force between particles and substrate. Pomorska et al. observed the positive resonant frequency shift when large diameter colloidal objects (>1 μm) were absorbed on QCM surface in liquid. Olofsson et al. used QCM to investigate the bacterial growth on the surface of stainless steel and found that the exponentially grown cells gave rise to a positive resonant frequency shift as long as their cell surface was hydrophilic. Dultsev and Kolosovsky mathematically demonstrated a positive resonant frequency shift caused by a single biological nano-sized particle. Castro et al. found a punctual rigid load applied on the QCM played as an apparent negative mass or resulting in positive frequency shift through both experiments and numerical simulation. Zhang et al. studied the deviations of frequency shift from Sauerbrey equation caused by finite size circular particles, and a frequency-dependent effective particle mass was introduced to classify and characterize different aspects of the particle-induced frequency shifts. Ramkrishnan et al. reported the positive frequency response when high aspect ratio structures were fabricated over surface acoustic wave (SAW) sensors, Olsson et al. classified the particle loading on QCM as “inertial loading” and “elastic loading”. The inertial loading resulted in a negative resonant frequency shift as described by Sauerbrey's theory while the “elastic loading” yielded a positive resonant frequency shift due to the coupled vibration. A coupled-resonance model was developed to quantitatively investigate the positive resonant frequency shift with elastic loading of particles. In this two-degree of freedom system, the QCM was treated as the main resonator with resonant of f0, and the particle attached on QCM surface played as a second resonator with its RF, fs. When a micro size particle was loaded on QCM, the contact area was limited to a small value and cause “elastic loading”. Furthermore, the resonant frequency of the particle attached to QCM is much smaller than that of original QCM, which results in a reduced resonant frequency of the coupled system. In this case, the positive resonant frequency shift become possible, which was proportional to the stiffness/elasticity of contact rather than the mass of particles.
There is a need for systems and methods that provide improved sensitivity.